{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T14:46:29Z","timestamp":1777128389024,"version":"3.51.4"},"publisher-location":"Cham","reference-count":45,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031334870","type":"print"},{"value":"9783031334887","type":"electronic"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"DOI":"10.1007\/978-3-031-33488-7_13","type":"book-chapter","created":{"date-parts":[[2023,5,28]],"date-time":"2023-05-28T16:01:43Z","timestamp":1685289703000},"page":"339-362","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Pairings in\u00a0Rank-1 Constraint Systems"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2873-3479","authenticated-orcid":false,"given":"Youssef El","family":"Housni","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,5,29]]},"reference":[{"key":"13_CR1","doi-asserted-by":"publisher","unstructured":"Aranha, D.F., Barreto, P.S.L.M., Longa, P., Ricardini, J.E.: The realm of the pairings. In: Lange, T., Lauter, K., Lisonek, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 3\u201325. Springer, Heidelberg (Aug 2014). https:\/\/doi.org\/10.1007\/978-3-662-43414-7_1","DOI":"10.1007\/978-3-662-43414-7_1"},{"key":"13_CR2","doi-asserted-by":"publisher","unstructured":"Aranha, D.F., Fuentes-Casta\u00f1eda, L., Knapp, E., Menezes, A., Rodr\u00edguez-Henr\u00edquez, F.: Implementing pairings at the 192-bit security level. In: Abdalla, M., Lange, T. (eds.) PAIRING 2012. LNCS, vol. 7708, pp. 177\u2013195. Springer, Heidelberg (May 2013). https:\/\/doi.org\/10.1007\/978-3-642-36334-4_11","DOI":"10.1007\/978-3-642-36334-4_11"},{"key":"13_CR3","doi-asserted-by":"crossref","unstructured":"Aranha, D.F., Housni, Y.E., Guillevic, A.: A survey of elliptic curves for proof systems. Cryptology ePrint Archive, Paper 2022\/586 (2022), https:\/\/eprint.iacr.org\/2022\/586","DOI":"10.1007\/s10623-022-01135-y"},{"key":"13_CR4","doi-asserted-by":"publisher","unstructured":"Aranha, D.F., Karabina, K., Longa, P., Gebotys, C.H., L\u00f3pez-Hern\u00e1ndez, J.C.: Faster explicit formulas for computing pairings over ordinary curves. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 48\u201368. Springer, Heidelberg (May 2011). https:\/\/doi.org\/10.1007\/978-3-642-20465-4_5","DOI":"10.1007\/978-3-642-20465-4_5"},{"key":"13_CR5","doi-asserted-by":"publisher","unstructured":"Barreto, P.S.L.M., Kim, H.Y., Lynn, B., Scott, M.: Efficient algorithms for pairing-based cryptosystems. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 354\u2013368. Springer, Heidelberg (Aug 2002). https:\/\/doi.org\/10.1007\/3-540-45708-9_23","DOI":"10.1007\/3-540-45708-9_23"},{"key":"13_CR6","doi-asserted-by":"publisher","unstructured":"Barreto, P.S.L.M., Lynn, B., Scott, M.: Constructing elliptic curves with prescribed embedding degrees. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol. 2576, pp. 257\u2013267. Springer, Heidelberg (Sep 2003). https:\/\/doi.org\/10.1007\/3-540-36413-7_19","DOI":"10.1007\/3-540-36413-7_19"},{"key":"13_CR7","unstructured":"Ben-Sasson, E., Chiesa, A., Tromer, E., Virza, M., Wu, H., Contributors: C++ library for zksnark, www.github.com\/scipr-lab\/libsnark"},{"key":"13_CR8","doi-asserted-by":"publisher","unstructured":"Boneh, D., Goh, E.J., Nissim, K.: Evaluating 2-DNF formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 325\u2013341. Springer, Heidelberg (Feb 2005). https:\/\/doi.org\/10.1007\/978-3-540-30576-7_18","DOI":"10.1007\/978-3-540-30576-7_18"},{"key":"13_CR9","doi-asserted-by":"publisher","unstructured":"Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514\u2013532. Springer, Heidelberg (Dec 2001). https:\/\/doi.org\/10.1007\/3-540-45682-1_30","DOI":"10.1007\/3-540-45682-1_30"},{"key":"13_CR10","doi-asserted-by":"publisher","unstructured":"Botrel, G., Piellard, T., Housni, Y.E., Kubjas, I., Tabaie, A.: Consensys\/gnark (Feb 2022). https:\/\/doi.org\/10.5281\/zenodo.6093969","DOI":"10.5281\/zenodo.6093969"},{"key":"13_CR11","doi-asserted-by":"publisher","unstructured":"Bowe, S., Chiesa, A., Green, M., Miers, I., Mishra, P., Wu, H.: ZEXE: Enabling decentralized private computation. In: 2020 IEEE Symposium on Security and Privacy, pp. 947\u2013964. IEEE Computer Society Press (May 2020). https:\/\/doi.org\/10.1109\/SP40000.2020.00050","DOI":"10.1109\/SP40000.2020.00050"},{"key":"13_CR12","unstructured":"Bowe, S., Grigg, J., Hopwood, D.: Halo: Recursive proof composition without a trusted setup. Cryptology ePrint Archive, Report 2019\/1021 (2019), https:\/\/eprint.iacr.org\/2019\/1021"},{"key":"13_CR13","doi-asserted-by":"publisher","unstructured":"Chiesa, A., Hu, Y., Maller, M., Mishra, P., Vesely, N., Ward, N.P.: Marlin: Preprocessing zkSNARKs with universal and updatable SRS. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part I. LNCS, vol. 12105, pp. 738\u2013768. Springer, Heidelberg (May 2020). https:\/\/doi.org\/10.1007\/978-3-030-45721-1_26","DOI":"10.1007\/978-3-030-45721-1_26"},{"key":"13_CR14","doi-asserted-by":"publisher","unstructured":"Chung, J., Hasan, M.A.: Asymmetric squaring formulae. In: 18th IEEE Symposium on Computer Arithmetic (ARITH 2007), pp. 113\u2013122 (2007). https:\/\/doi.org\/10.1109\/ARITH.2007.11","DOI":"10.1109\/ARITH.2007.11"},{"key":"13_CR15","unstructured":"arkworks Contributors: arkworks zkSNARK ecosystem. https:\/\/arkworks.rs (2022)"},{"key":"13_CR16","doi-asserted-by":"publisher","unstructured":"Costello, C., Lange, T., Naehrig, M.: Faster pairing computations on curves with high-degree twists. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 224\u2013242. Springer, Heidelberg (May 2010). https:\/\/doi.org\/10.1007\/978-3-642-13013-7_14","DOI":"10.1007\/978-3-642-13013-7_14"},{"key":"13_CR17","doi-asserted-by":"publisher","unstructured":"Eisentr\u00e4ger, K., Lauter, K., Montgomery, P.L.: Fast elliptic curve arithmetic and improved Weil pairing evaluation. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 343\u2013354. Springer, Heidelberg (Apr 2003). https:\/\/doi.org\/10.1007\/3-540-36563-X_24","DOI":"10.1007\/3-540-36563-X_24"},{"key":"13_CR18","doi-asserted-by":"publisher","unstructured":"El Housni, Y., Guillevic, A.: Families of SNARK-friendly 2-chains of elliptic curves. In: Dunkelman, O., Dziembowski, S. (eds.) EUROCRYPT 2022. LNCS, vol. 13276, pp. 367\u2013396. Springer (2022). https:\/\/doi.org\/10.1007\/978-3-031-07085-3_13, ePrint https:\/\/eprint.iacr.org\/2021\/1359","DOI":"10.1007\/978-3-031-07085-3_13,"},{"key":"13_CR19","unstructured":"Gabizon, A., Williamson, Z.J., Ciobotaru, O.: PLONK: Permutations over lagrange-bases for oecumenical noninteractive arguments of knowledge. ePrint https:\/\/eprint.iacr.org\/2019\/953"},{"key":"13_CR20","unstructured":"Ghammam, L., Fouotsa, E.: On the computation of the optimal ate pairing at the 192-bit security level. Cryptology ePrint Archive, Report 2016\/130 (2016), https:\/\/eprint.iacr.org\/2016\/130"},{"key":"13_CR21","doi-asserted-by":"publisher","unstructured":"Granger, R., Scott, M.: Faster squaring in the cyclotomic subgroup of sixth degree extensions. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 209\u2013223. Springer, Heidelberg (May 2010). https:\/\/doi.org\/10.1007\/978-3-642-13013-7_13","DOI":"10.1007\/978-3-642-13013-7_13"},{"key":"13_CR22","doi-asserted-by":"publisher","unstructured":"Grewal, G., Azarderakhsh, R., Longa, P., Hu, S., Jao, D.: Efficient implementation of bilinear pairings on ARM processors. In: Knudsen, L.R., Wu, H. (eds.) SAC 2012. LNCS, vol. 7707, pp. 149\u2013165. Springer, Heidelberg (Aug 2013). https:\/\/doi.org\/10.1007\/978-3-642-35999-6_11","DOI":"10.1007\/978-3-642-35999-6_11"},{"key":"13_CR23","doi-asserted-by":"publisher","unstructured":"Groth, J.: Short pairing-based non-interactive zero-knowledge arguments. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321\u2013340. Springer, Heidelberg (Dec 2010). https:\/\/doi.org\/10.1007\/978-3-642-17373-8_19","DOI":"10.1007\/978-3-642-17373-8_19"},{"key":"13_CR24","doi-asserted-by":"publisher","unstructured":"Groth, J.: On the size of pairing-based non-interactive arguments. In: Fischlin, M., Coron, J.S. (eds.) EUROCRYPT 2016, Part II. LNCS, vol. 9666, pp. 305\u2013326. Springer, Heidelberg (May 2016). https:\/\/doi.org\/10.1007\/978-3-662-49896-5_11","DOI":"10.1007\/978-3-662-49896-5_11"},{"key":"13_CR25","doi-asserted-by":"publisher","unstructured":"Groth, J., Kohlweiss, M., Maller, M., Meiklejohn, S., Miers, I.: Updatable and universal common reference strings with applications to zk-SNARKs. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part III. LNCS, vol. 10993, pp. 698\u2013728. Springer, Heidelberg (Aug 2018). https:\/\/doi.org\/10.1007\/978-3-319-96878-0_24","DOI":"10.1007\/978-3-319-96878-0_24"},{"key":"13_CR26","doi-asserted-by":"publisher","unstructured":"Groth, J., Ostrovsky, R., Sahai, A.: Non-interactive zaps and new techniques for NIZK. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 97\u2013111. Springer, Heidelberg (Aug 2006). https:\/\/doi.org\/10.1007\/11818175_6","DOI":"10.1007\/11818175_6"},{"key":"13_CR27","doi-asserted-by":"publisher","unstructured":"Guillevic, A., Masson, S., Thom\u00e9, E.: Cocks-Pinch curves of embedding degrees five to eight and optimal ate pairing computation. Des. Codes Cryptogr. 88, 1047\u20131081 (March 2020). https:\/\/doi.org\/10.1007\/s10623-020-00727-w","DOI":"10.1007\/s10623-020-00727-w"},{"key":"13_CR28","unstructured":"Hayashida, D., Hayasaka, K., Teruya, T.: Efficient final exponentiation via cyclotomic structure for pairings over families of elliptic curves. ePrint https:\/\/eprint.iacr.org\/2020\/875"},{"key":"13_CR29","doi-asserted-by":"publisher","unstructured":"Housni, Y.E., Guillevic, A.: Optimized and secure pairing-friendly elliptic curves suitable for one layer proof composition. In: Krenn, S., Shulman, H., Vaudenay, S. (eds.) CANS 20. LNCS, vol. 12579, pp. 259\u2013279. Springer, Heidelberg (Dec 2020). https:\/\/doi.org\/10.1007\/978-3-030-65411-5_13","DOI":"10.1007\/978-3-030-65411-5_13"},{"issue":"281","key":"13_CR30","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1090\/S0025-5718-2012-02625-1","volume":"82","author":"K Karabina","year":"2013","unstructured":"Karabina, K.: Squaring in cyclotomic subgroups. Math. Comput. 82(281), 555\u2013579 (2013). https:\/\/doi.org\/10.1090\/S0025-5718-2012-02625-1","journal-title":"Math. Comput."},{"key":"13_CR31","unstructured":"Karatsuba, A., Ofman, Y.: Multiplication of Multidigit Numbers on Automata. Soviet Physics Doklady 7, 595 (1963)"},{"key":"13_CR32","doi-asserted-by":"publisher","unstructured":"Kate, A., Zaverucha, G.M., Goldberg, I.: Constant-size commitments to polynomials and their applications. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 177\u2013194. Springer, Heidelberg (Dec 2010). https:\/\/doi.org\/10.1007\/978-3-642-17373-8_11","DOI":"10.1007\/978-3-642-17373-8_11"},{"key":"13_CR33","unstructured":"Kosba, A., et al.: C$$\\emptyset $$c$$\\emptyset $$: A framework for building composable zero-knowledge proofs. Cryptology ePrint Archive, Report 2015\/1093 (2015), https:\/\/eprint.iacr.org\/2015\/1093"},{"key":"13_CR34","unstructured":"Liochon, N., Chapuis-Chkaiban, T., Belling, A., Begassat, O.: A zk-evm specification. https:\/\/ethresear.ch\/t\/a-zk-evm-specification\/11549 (2021)"},{"key":"13_CR35","unstructured":"Longa, P.: Efficient algorithms for large prime characteristic fields and their application to bilinear pairings and supersingular isogeny-based protocols. Cryptology ePrint Archive, Report 2022\/367 (2022), https:\/\/eprint.iacr.org\/2022\/367"},{"key":"13_CR36","doi-asserted-by":"publisher","unstructured":"Maller, M., Bowe, S., Kohlweiss, M., Meiklejohn, S.: Sonic: Zero-knowledge SNARKs from linear-size universal and updatable structured reference strings. In: Cavallaro, L., Kinder, J., Wang, X., Katz, J. (eds.) ACM CCS 2019, pp. 2111\u20132128. ACM Press (Nov 2019). https:\/\/doi.org\/10.1145\/3319535.3339817","DOI":"10.1145\/3319535.3339817"},{"key":"13_CR37","doi-asserted-by":"publisher","unstructured":"Miller, V.S.: The Weil pairing, and its efficient calculation. J. Cryptolo. 17(4), 235\u2013261 (2004). https:\/\/doi.org\/10.1007\/s00145-004-0315-8","DOI":"10.1007\/s00145-004-0315-8"},{"key":"13_CR38","doi-asserted-by":"crossref","unstructured":"Miyaji, A., Nakabayashi, M., Takano, S.: Characterization of elliptic curve traces under FR-reduction. In: Won, D. (ed.) ICISC 2000. LNCS, vol. 2015, pp. 90\u2013108. Springer, Heidelberg (Dec 2001)","DOI":"10.1007\/3-540-45247-8_8"},{"key":"13_CR39","doi-asserted-by":"crossref","unstructured":"Naehrig, M., Barreto, P.S.L.M., Schwabe, P.: On compressible pairings and their computation. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 371\u2013388. Springer, Heidelberg (Jun 2008)","DOI":"10.1007\/978-3-540-68164-9_25"},{"key":"13_CR40","doi-asserted-by":"publisher","unstructured":"Rubin, K., Silverberg, A.: Torus-based cryptography. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 349\u2013365. Springer, Heidelberg (Aug 2003). https:\/\/doi.org\/10.1007\/978-3-540-45146-4_21","DOI":"10.1007\/978-3-540-45146-4_21"},{"key":"13_CR41","unstructured":"Scott, M.: Pairing implementation revisited. ePrint https:\/\/eprint.iacr.org\/2019\/077"},{"key":"13_CR42","unstructured":"Scott, M.: A note on twists for pairing friendly curves (2009), http:\/\/indigo.ie\/~mscott\/twists.pdf"},{"key":"13_CR43","unstructured":"Stam, M.: XTR and tori. Cryptology ePrint Archive, Report 2021\/1659 (2021), https:\/\/eprint.iacr.org\/2021\/1659"},{"issue":"1","key":"13_CR44","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1109\/TIT.2009.2034881","volume":"56","author":"F Vercauteren","year":"2010","unstructured":"Vercauteren, F.: Optimal pairings. IEEE Trans. Inf. Theor. 56(1), 455\u2013461 (2010). https:\/\/doi.org\/10.1109\/TIT.2009.2034881","journal-title":"IEEE Trans. Inf. Theor."},{"key":"13_CR45","unstructured":"Xiong, A.L., et al.: VERI-ZEXE: Decentralized private computation with universal setup. Cryptology ePrint Archive, Report 2022\/802 (2022), https:\/\/eprint.iacr.org\/2022\/802"}],"container-title":["Lecture Notes in Computer Science","Applied Cryptography and Network Security"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-33488-7_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,28]],"date-time":"2023-05-28T16:02:59Z","timestamp":1685289779000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-33488-7_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031334870","9783031334887"],"references-count":45,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-33488-7_13","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"29 May 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ACNS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Applied Cryptography and Network Security","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Kyoto","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Japan","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 June 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 June 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"acns2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/sulab-sever.u-aizu.ac.jp\/ACNS2023\/committees.html","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"easychair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"263","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"53","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"20% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.9","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"14.2","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}